具有梳齿状结构的基尔霍夫-洛夫板的无效内部可控性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-09-04 DOI:10.1137/24m1647825

Umberto De Maio, Antonio Gaudiello, Cătălin-George Lefter

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 5 期第 2456-2474 页，2024 年 10 月。摘要本文致力于研究具有梳状结构的 Kirchoff-Love 薄板的空内可控性，该薄板的中间表面具有大量由小正向参数描述的薄指[math]。由于薄指数量众多，通常无法直接用数值方法来解决此类问题。因此需要进行渐近分析。在本文中，我们首先证明该问题在每个层次上都是空可控的[数学]。然后我们证明，当[math]消失时，具有最小[math]规范的相应控制序列收敛于一个极限控制函数，该函数确保了无指域中退化极限问题集的最优空可控性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Null Internal Controllability for a Kirchhoff–Love Plate with a Comb-Like Shaped Structure

SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 2456-2474, October 2024.
Abstract. This paper is devoted to studying the null internal controllability of a Kirchoff–Love thin plate with a middle surface having a comb-like shaped structure with a large number of thin fingers described by a small positive parameter [math]. It is often impossible to directly approach such a problem numerically, due to the large number of thin fingers. So an asymptotic analysis is needed. In this paper, we first prove that the problem is null controllable at each level [math]. We then prove that the sequence of the respective controls with minimal [math] norm converges, as [math] vanishes, to a limit control function ensuring the optimal null controllability of a degenerate limit problem set in a domain without fingers.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.